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This book covers functional analysis and its applications to continuum mechanics. The mathematical material is treated in a non-abstract manner and is fully illuminated by the underlying mechanical ideas. The presentation is concise but complete, and is intended for specialists in continuum mechanics who wish to understand the mathematical underpinnings of the discipline. Graduate students and researchers in mathematics, physics, and engineering will find this book useful. Exercises and examples are included throughout with detailed solutions provided in the appendix.
List of contents
Metric Spaces Elements of theory of operators Elements of nonlinear functional analysis Hints for selected problems
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From the reviews: "The material in this book is a mixture of functional analysis, presented at the level of a mathematics students, and (mechanical) engineering applications. It is a concise but complete treatment of the abstract notions underlying problems in continuum mechanics. It grew out of 30 years of experience of the authors and it is a welcome translation of Russian edition. It will be highly appreciated by graduate students in mathematics, physics and engineering." (Adhemar Bultheel, Bulletin of the Belgian Mathematical Society, Vol. 12 (1), 2005) "The book is a revised and extended translation of the Russian edition. The book is suitable for readers in continuum mechanics and can be recommended to graduate students and researchers in mathematics, physics and engineering." (EMS European Mathematical Society Newsletter, March, 2004) "This book covers functional analysis and its applications to continuum mechanics. The presentation is concise but complete, and is intended for readers in continuum mechanics who wish to understand the mathematical underpinnings of the discipline. Detailed solutions of the exercises are provided in an appendix." (L Enseignment Mathematique, Vol. 49 (1-2), 2003) "The reader comes away with a profound appreciation both of the physics and its importance, and of the beauty of the functional analytic method, which, in skillful hands, has the power to dissolve and clarify these difficult problems as peroxide does clotted blood. Numerous exercises test the reader s comprehension at every stage. Summing Up: Recommended." (F. E. J. Linton, Choice, September, 2003) "The formulated applications are by all means interesting. It is also very good that more complicated problems have been included. The book gives a survey of material which every worker in applications of functional analysis to various parts of mechanics should know." (Rudolf Kodnr, Zentralblatt MATH, Vol. 1014, 2003) "This textbook is based on the course of lectures on functional analysis . General ideas and algorithms are clear and understandable. There is a good index attached. This skillfully-written book is a reader friendly and well-organized textbook in the field of Mathematical Mechanics. It can be highly recommended for students of technology universities as well as for researchers in Mechanics. The book is recommended for purchase by university libraries and for individuals interested in the mathematical problems of Mechanics." (I Andrianov, Applied Mechanics Reviews, Vol. 56 (4), 2003)
